Nov 3 (Reuters) - A surge in oil prices fueled a rally in energy companies, helping the S&P and Nasdaq reverse course to move higher in afternoon trading on Tuesday, while the Dow added to its gains.

The energy sector rose 2.6 percent, easily the best among the 10 major S&P sectors, putting the sector on track for its best five-day run in nearly a month.

Five of the 10 S&P sectors were lower, led by the consumer staples sector’s 0.79 percent drop. As many as eight sectors were lower when the market opened.

Exxon’s shares were up 2 percent and Chevron’s 3.5 percent, and both stocks were among the top influences on the Dow and S&P.

Visa was another, with the stock up 3.6 percent to $77.95, after a 3 percent drop on Monday when it said it would buy Visa Europe.

Activision Blizzard surged 7 percent to $37 and was the fourth biggest boost on the Nasdaq. The stock was down earlier after the video games maker said it would buy “Candy Crush” maker King Digital for $5.9 billion. King soared 14.8 percent to $17.84.

At 13:07 a.m. ET (1607 GMT), the Dow Jones industrial average was up 88.05 points, or 0.49 percent, at 17,916.81.

The S&P 500 was up 4.86 points, or 0.23 percent, at 2,108.91 and the Nasdaq Composite index was up 20.94 points, or 0.41 percent, at 5,148.09.

“I don’t think there’s really any big momentum one way or the other with the earnings,” said Michael Bapis, managing director and partner at Hightower’s the Bapis Group.

The two key influences on the market this week would be Federal Reserve Chair Janet Yellen’s testimony before the House Financial Services Committee on Wednesday and the monthly jobs report on Friday, said Bapis.

A majority of the S&P 500 companies have reported strong third-quarter results. Their profit is now expected to have dipped 1.5 percent, compared with the 4.9 percent drop forecast before the earnings season began, Thomson Reuters data shows.

Of the 379 S&P 500 companies that have reported results so far, 70 percent have beaten profit estimates, compared with 63 percent in a typical quarter.

Not so with AIG.

AIG fell 4.3 percent to $60.98 after the insurer’s quarterly profit missed estimates by a wide margin. CEO Peter Hancock said Carl Icahn’s proposal to break up the company did not “make financial sense”.

Agribusiness Archer Daniels Midland dropped 8.8 percent to $42.20 after missing profit estimates. Altria fell 4 percent to $57.98 after a rating cut. The two were the biggest drags on the consumer staples sector.

Fitbit slid 5.7 percent to $38.48 after the wearable fitness device maker said it would lift a restriction on share lockup before scheduled and announced a share offering.

Advancing issues outnumbered decliners on the NYSE by 1,742 to 1,250. On the Nasdaq, 1,775 issues rose and 959 fell.

The S&P 500 index showed 13 new 52-week highs and one new low, while the Nasdaq recorded 65 new highs and 18 new lows. (Reporting by Abhiram Nandakumar in Bengaluru; Editing by Savio D‘Souza)